Electron Transfer of Hydrated Transition-Metal Ions and the Electronic State of Co³⁺(aq)

Abstract

Electron transfer (ET) is broadly described by Marcus-type theories and plays a central role in many materials and catalytic systems and in biomolecules such as cytochromes. Classic ET processes are the self-exchange reactions between hydrated transition-metal ions such as Fe(aq) + Fe(aq) → Fe(aq) + Fe(aq). A well-known anomaly of Marcus theory is Co/Co exchange, which proceeds ∼10 times faster than predicted. Co(aq) is a complex and reactive system widely thought to feature low-spin Co. We studied the self-exchange process systematically for Cr/Cr, V/V, Fe/Fe, and Co/Co using six distinct density functionals. We identify directly the ∼10 anomaly of Co/Co from the electronic reorganization energies without the use of empirical cross-relations. Furthermore, when Co is modeled as high-spin, the anomaly disappears, bringing all four processes on a linear trend within the uncertainty of the experiments and theory. We studied both the acid-independent [Co(HO)] species that dominates at low pH and the acid-dependent [Co(OH)(HO)] species that becomes important at higher pH and used two distinct explicit second-sphere hydration models and models of perchlorate anion association. The high-spin state with weaker Co-O bonds is stabilized by vibrational energy and entropy by ∼11 and ∼12 kJ mol, correcting the gap estimates from absorption spectroscopy. High-spin Co(aq) explains the full experimental data series of the M(aq) systems. Low-spin Co and high-spin Co involve changes in the e occupation upon ET with associated M-O bond changes and increased reorganization energy. In contrast, with high-spin Co(aq), the redox-active electrons shuffle between t orbitals to minimize structural changes, producing a relative rate in excellent agreement with the experiments. This e occupation effect explains most of the experimental differences in the rate constants, with the remaining part explained by second-sphere hydration and anion effects. Our results consistently suggest that some high-spin Co(aq) is active during the experiments.

Free Energies of Hydration for Metal Ions from Heats of Vaporization

“…A notable example is the deprotonation of a water of the first coordination shell of the M 3+ ions caused by the Brønsted acidity of these aqua complexes, and the hydrolytic instability and possibly mixed nature of some species such as Co 3+ (aq). 54 Since all data reported here are based on the active species in solution that give rise to the observed values, this does not affect the accuracy of the tabulated data. However, variations in chemical composition and coordination number will potentially weaken the trend chemistry 55 as discussed further below.…”

The Chemical Bond between Transition Metals and Oxygen: Electronegativity, d-Orbital Effects, and Oxophilicity as Descriptors of Metal–Oxygen Interactions

“…However, the oxophilicity correlates strongly with a chemical reactivity across the d-transition metals and rationalize both ore mineralization and catalytic activity in a wide range of reactions. 15 Similarly, the periodic and orbital trends of 20 the first coordination sphere defines the chemical reactivity and free energies of hydration of the transition metal ions in water 60,72 , which reflect condense systems. Finally, Figure 4D shows that CCSD(T) BDEs also correlate highly significantly with the oxophilicity (p = 2.6 • 10 -10 ).…”

Contribution of substrate reorganization energies of electron transfer to laccase activity

“…Thus, our results are not very sensitive to the choice of functional. This conclusion is, importantly, specific to the computation of λ where four energy evaluations work to cancel the effects of the different functionals, making these computations very robust and useful for the evaluation of trend chemistry vs. experimental data, as seen previously 42 . A similar conclusion applies to dataset B after removal of the difficult outliers (Figure 3).…”

“…The geometries need to be well-described, in particular by also including polarization functions on hydrogen atoms. It is considered more important to compute the single point energies at the exact same level of theory as the geometry optimized ground states in order to estimate the vertical ionization energies and electron affinities correctly, otherwise a shift of the potential energy curve would occur 42 . This study includes 108 geometry optimizations of compounds of very variable size, and thus we used the 6-31G** basis set that includes polarization functions on all atoms, estimating that basis set errors, which tend to cancel in the four energies once combined, is of the order of 1-3 kcal/mol and will thus not affect the trends described below in the results section, which are governed by changes up to typically 20-30 kcal/mol.…”

“…38 Galli et al previously studied the oxidation by laccases from Trametes villosa, T. versicolor and a T. versicolor D206A mutant of six phenolic substrates and in this process accounted for the importance of λ. 22 The T1 λ is ~0.5-0.8 eV and similar for T1 sites of different proteins with the same coordination geometry [39][40][41] , as λ is dominated by the inner-sphere component of the first coordination sphere 17,42,43 . Thus, any contribution of λ to relative experimental activities should arise via the substrate's self-exchange λ.…”